Mathematics Commons^™

Counting The Moduli Space Of Pentagons On Finite Projective Planes, Maxwell Hosler

Senior Independent Study Theses

Finite projective planes are finite incidence structures which generalize the concept of the real projective plane. In this paper, we consider structures of points embedded in these planes. In particular, we investigate pentagons in general position, meaning no three vertices are colinear. We are interested in properties of these pentagons that are preserved by collineation of the plane, and so can be conceived as properties of the equivalence class of polygons up to collineation as a whole. Amongst these are the symmetries of a pentagon and the periodicity of the pentagon under the pentagram map, and a generalization of …

Wildfire Simulation Using Agent Based Modeling: Expanding Controlled Burn Season, Morgan C. Kromer

Senior Independent Study Theses

The United States is home to many different and unique forests. Prior to the 21st century, the United States Forests Service assumed that the best way to protect these forests was to put all efforts to keeping them alive. An enemy to these efforts were wildfires, thus the US adopted a complete fire suppression approach. At the turn of the century, the US realized that wildfires are a necessary part of a forest ecosystem, as they help return nutrients to the soil and reduce ground fuels. However, after suppressing all fires for over 100 years, the forests evolved into a …

Optimizing Model Observer Performance In Learning-Based Ct Reconstruction, Gregory Ongie, Emil Y. Sidky, Ingrid S. Reiser, Xiaochuan Pan

Mathematical and Statistical Science Faculty Research and Publications

Deep neural networks used for reconstructing sparse-view CT data are typically trained by minimizing a pixel- wise mean-squared error or similar loss function over a set of training images. However, networks trained with such losses are prone to wipe out small, low-contrast features that are critical for screening and diagnosis. To remedy this issue, we introduce a novel training loss inspired by the model observer framework to enhance the detectability of weak signals in the reconstructions. We evaluate our approach on the reconstruction of synthetic sparse-view breast CT data, and demonstrate an improvement in signal detectability with the proposed loss.

Bft2: A General Class Of 2d N = (0, 2) Theories, 3-Manifolds And Toric Geometry, Sebastían Franco, Xingyang Yu

Publications and Research

We introduce and initiate the study of a general class of 2d N = (0, 2) quiver gauge theories, defined in terms of certain 2-dimensional CW complexes on oriented 3- manifolds. We refer to this class of theories as BFT₂’s. They are natural generalizations of Brane Brick Models, which capture the gauge theories on D1-branes probing toric Calabi-Yau 4-folds. The dynamics and triality of the gauge theories translate into simple transformations of the underlying CW complexes. We introduce various combinatorial tools for analyzing these theories and investigate their connections to toric Calabi-Yau manifolds, which arise as their …

2d N = (0, 1) Gauge Theories And Spin(7) Orientifolds, Sebastían Franco, Alessandro Mininno, Ángel M. Uranga, Xingyang Yu

Publications and Research

We initiate the geometric engineering of 2d N = (0, 1) gauge theories on D1-branes probing singularities. To do so, we introduce a new class of backgrounds obtained as quotients of Calabi-Yau 4-folds by a combination of an anti-holomorphic involution leading to a Spin(7) cone and worldsheet parity. We refer to such constructions as Spin(7) orientifolds. Spin(7) orientifolds explicitly realize the perspective on 2d N = (0, 1) theories as real slices of N = (0, 2) ones. Remarkably, this projection is geometrically realized as Joyce’s construction of Spin(7) manifolds via quotients of Calabi-Yau 4-folds by antiholomorphic …

Reinforcement Learning: Low Discrepancy Action Selection For Continuous States And Actions, Jedidiah Lindborg

College of Graduate Studies: Theses & Dissertations

In reinforcement learning the process of selecting an action during the exploration or exploitation stage is difficult to optimize. The purpose of this thesis is to create an action selection process for an agent by employing a low discrepancy action selection (LDAS) method. This should allow the agent to quickly determine the utility of its actions by prioritizing actions that are dissimilar to ones that it has already picked. In this way the learning process should be faster for the agent and result in more optimal policies.

On The Geometry Of The Multiplier Space Of ℓPA, Christopher Felder, Raymond Cheng

Mathematics & Statistics Faculty Publications

For p ∊ (1, ∞)\ {2}, some properties of the space M_p of multipliers on ℓ^p_A are derived. In particular, the failure of the weak parallelogram laws and the Pythagorean inequalities is demonstrated for M_p. It is also shown that extremal multipliers on the ℓ^p_A spaces are exactly the monomials, in stark contrast to the p = 2 case.

Cloud Ripple Pattern, John Adam

Mathematics & Statistics Faculty Publications

No abstract provided.

Rock Paintings: Solutions For Fermi Questions, September 2022, John Adam

Mathematics & Statistics Faculty Publications

No abstract provided.

Jacobi's Four Squares Theorem, Arman Yagci

Honors Papers

Jacobi’s Four Squares Theorem is a celebrated result of number theory that provides a formula for the number of ways a positive integer n can be written as a sum of four integral squares. In this paper, we prove this theorem using the theory of modular forms.

Question 1: Space Telescope; Question 2: Jwst2, Larry Weinstein

Physics Faculty Publications

[Introduction] Space telescope

Question 1: If the James Webb Space Telescope could be turned to face Earth, how small an object could it resolve? How does that compare to the Hubble Space Telescope? ...

Question 2: How much heat from Earth is blocked by the Sun and Earth shade of the James Webb Space Telescope? ...

Question: While I was at a Norfolk Tides baseball game, a foul ball landed in the section above me and showered some of my friends with beer. What is the probability of a foul ball landing directly in a cup of beer during one …

Solutions For Fermi Questions, May 2022, Larry Weinstein

Physics Faculty Publications

[Introduction] Question: If the James Webb Space Telescope could be turned to face the Earth, how small an object could it resolve? How does that compare to the Hubble Space Telescope?.

To answer this, we need to know the location of the JWST, its size, and the wavelengths it can image. (This is one of those Fermi questions where we're not really estimating, but we are calculating unusual order-of-magnitude answers.) The JWST is orbiting the Earth and Sun at the second Lagrange point, L2, which is located 1.5 × 10⁶ km beyond the Earth (so that the Sun, Earth and …

Question 1: Ketchup Packets; Question 2: Dog Hair, Larry Weinstein

Physics Faculty Publications

Question 2: Dog hair How much dog hair is shed (and subsequently vacuumed) in the U.S. each year? How many ketchup packets are used in America every year?.

Contractible 4-Manifolds, Alexandra Du

Honors Papers

Compact, contractible 4-manifolds distinct from D^4 were first constructed by Mazur and Poénaru. Sparks defined a collection of compact, contractible 4-manifolds called Jester manifolds. We study Mazur and Jester 4-manifolds. In particular, we show that all Jester manifolds are not homeomorphic to D^4, and that a collection of them are pairwise nonhomeomorphic.

Exo-Sir: An Epidemiological Model To Analyze The Impact Of Exogenous Spread Of Infection, Nirmal Kumar Sivaraman, Manas Gaur, Shivansh Baijal, Sakthi Balan Muthiah, Amit Sheth

Publications

Epidemics like Covid-19 and Ebola have impacted people's lives significantly. The impact of mobility of people across the countries or states in the spread of epidemics has been significant. The spread of disease due to factors local to the population under consideration is termed the endogenous spread. The spread due to external factors like migration, mobility, etc. is called the exogenous spread. In this paper, we introduce the Exo-SIR model, an extension of the popular SIR model and a few variants of the model. The novelty in our model is that it captures both the exogenous and endogenous spread of …

Finite Index Right-Angled Mock Artin Groups In Right-Angled Mock Reflection Groups, Zachary Marcum

Murray State Theses and Dissertations

Associated to any graph Γ are several groups where their presentations are encoded by Γ. Two such groups are right-angled Coxeter groups and right-angled Artin groups. By introducing more structure to Γ, what we call "local involutions," the graph Γ becomes a right-angled mock reflection system and encodes the presentation of two more groups: right-angled mock reflection groups and right-angled mock Artin groups.

Here we show that every right-angled mock Artin group associated with an n-gon graph with local involutions is a finite index subgroup in some right-angled mock reflection group. We employ a strategy similar to the one Davis …

Maintenance Optimization In A Digital Twin For Industry 4.0, Abhijit Gosavi, Vy Khoi Le

Engineering Management and Systems Engineering Faculty Research & Creative Works

The advent of Internet of Things and artificial intelligence in the era of Industry 4.0 has transformed decision-making within production systems. In particular, many decisions that previously required significant human activity are now made automatically with minimal human intervention via so-called digital twins (DTs). In the context of maintenance and reliability modeling, this naturally calls for new paradigms that can be seamlessly integrated within DTs for decision-making. The input data for time to failure needed in reliability computations are directly collected from the work center in a digital setting and often do not satisfy a known distribution. A neural network …

Dynamics Of Mutualism In A Two Prey, One Predator System With Variable Carrying Capacity, Randy Huy Lee

UNF Graduate Theses and Dissertations

We considered the livelihood of two prey species in the presence of a predator species. To understand this phenomenon, we developed and analyzed two mathematical models considering indirect and direct mutualism of two prey species and the influence of one predator species. Both types of mutualism are represented by an increase in the preys' carrying capacities based on direct and indirect interactions between the prey. Because of mutualism, as the death rate parameter of the predator species goes through some critical value, the model shows transcritical bifurcation. Additionally, in the direct mutualism model, as the death rate parameter decreases to …

Frequent Mental Distress Among Adults In The United States And Its Association With Socio-Demographic Characteristics, Unhealthy Lifestyle, And Chronic Physical Health Status, Mamunur Rashid, M. Mazharul Islam, Aiping Li, Naima Shifa

Mathematics Faculty Publications

Frequent mental distress (FMD) is a measure of poor mental health days for at least 14 days out of 30 days. It is one of the important dimensions of the health-related quality of life. The underlying causes of FMD are diverse. However, the issue has not been explored extensively due to the lack of reliable data on mental health. The aim of this study was to examine the level and trends of FMD among the adults of the United States (US) and identify the socio-demographic, lifestyles, and chronic health outcomes related correlates of FMD. The data for the study was …

Characterizing Properties Of Implicit Dependence Copulas And Extreme Copulas, Noppawit Yanpaisan

Chulalongkorn University Theses and Dissertations (Chula ETD)

No abstract provided.